NAG Library Function Document

nag_erf (s15aec)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

nag_erf (s15aec) returns the value of the error function,

\erf x

2 Specification

#include <nag.h>

#include <nags.h>

double

nag_erf (double x)

3 Description

nag_erf (s15aec) evaluates

\erf x = \frac{2}{\sqrt{π}} \int_{0}^{x} e^{- t^{2}} d t .

The approximation is based on Chebyshev expansions.

4 References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5 Arguments

1: x – doubleInput: On entry: the argument $x$ of the function.

6 Error Indicators and Warnings

None.

7 Accuracy

On a machine with approximately 11 significant figures the function agrees with available tables to 10 figures and consistency checking with nag_erfc (s15adc) of the relation

\erf x + erfc x = 1.0

shows errors in at worst the 11th figure.

8 Further Comments

None.

9 Example

The following program reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

NAG Library Function Documentnag_erf (s15aec)